Author(s)

D. Berzi, J. T. Jenkins & E. Larcan

Abstract

We simplify a two-phase theory proposed by Berzi and Jenkins for the uniform motion of a granular-fluid mixture to obtain explicit, analytical relations between the tangent of the angle of inclination of the free surface, the average particle (fluid) velocity and the particle (fluid) depth. Those expressions, valid, in principle, only in uniform flow conditions, can then be employed to express the motion resistance for the particles and the fluid in mathematical models of non-uniform flow, as customary in Hydraulics. The advantages of those formulas with regard to previous, widely employed expressions are also discussed. Keywords: rheology, uniform flow, friction slope. 1 Introduction Recently, Berzi and Jenkins [1–3] proposed a simple theory based on a linear rheology for the particle interactions, turbulent shearing of the fluid, buoyancy, and drag. They provided a complete analytical description of the steady, uniform flow of a granular-fluid mixture (debris flow) over an inclined bed contained between frictional sidewalls. In order to obtain such analytical solution, they assumed a constant concentration in the particle-fluid mixture and the similarity of the particle and fluid velocity profiles. The predictions of this description compared favourably with the measurements in experiments on steady, uniform granular-fluid flows performed by Armanini et al. [4] and Larcher et al. [5] on mono-dispersed plastic cylinders and water. As seen in the experiments, the particle and fluid velocity distributions, the flow depths, and the free surface

Keywords

rheology, uniform flow, friction slope